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Adiabatic and irreversible classical discrete time crystals
by Adrian Ernst, Anna M. E. B. Rossi, Thomas M. Fischer
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Submission summary
Authors (as registered SciPost users): | Adrian Ernst · Thomas Fischer · Anna M. E. B. Rossi |
Submission information | |
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Preprint Link: | https://arxiv.org/abs/2203.04063v1 (pdf) |
Date submitted: | 2022-03-09 07:35 |
Submitted by: | Fischer, Thomas |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
Specialties: |
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Approaches: | Theoretical, Computational |
Abstract
We simulate the dynamics of paramagnetic colloidal particles that are placed above a magnetic hexagonal pattern and exposed to an external field periodically changing its direction along a control loop. The conformation of three colloidal particles above one unit cell adiabatically responds with half the frequency of the external field creating a time crystal at arbitrary low frequency. The adiabatic time crystal occurs because of the non-trivial topology of the stationary manifold. When coupling colloidal particles in different unit cells, many body effects cause the formation of topologically isolated time crystals and dynamical phase transitions between different adiabatic reversible and non-adiabatic irreversible space-time-crystallographic arrangements.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 4) on 2022-7-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2203.04063v1, delivered 2022-07-10, doi: 10.21468/SciPost.Report.5373
Strengths
1- Glossy figures
2- Nice videos
Weaknesses
Difficult to follow
Report
The authors propose a realization of classical discrete time crystals in a system of paramagnetic colloidal particles that are placed above a magnetic hexagonal pattern and exposed to an external field that changes its direction periodically.
I have to admit that this work is a bit peripheral to my expertise. Thus, although it does seem interesting, I have confess that I have a bit of a hard time following it.
Part of the issue may be related to the figures that are glossy, but nevertheless difficult to understand.
Figure 1 is particularly difficult to understand. If its description would mention specific parts (left, middle, or right panel), this would probably already help. Likewise, section 2 is quite abstract and thus not easy to read, at least not for a non-expert.
Another detail is recurrent terminology such as "north pole". I only found a short explanation on page 5 during a careful second reading. At the same time, the angles $\vartheta$ and $\varphi$ are not properly introduced. Conversely, line 2 of the caption of Fig. 5 mentions a direction that is "normal to the pattern", which might be identical to "north".
The caption of Fig. 7 should mention that this space-time picture is for a chain of honeycomb cells.
The five accompanying video clips are extremely useful to clarify and illustrate the findings of the present work. However, I believe that it would be good to emphasize that these videos are not just a supplementary piece, but actually an important part of this work. At the same time, the source in Ref. [49] needs to be specified more clearly. It may be Ok to use arXiv for them, but since this is not SciPost, this should be stated explicitly.
Content-wise, the middle panel of Fig. 1 does not factorize into a control space ${\cal C}$ and an action space ${\cal A}$, as the notation ${\cal C} \otimes {\cal A}$ seems to suggest.
A further comment on content is the emphasis on the behavior at the edge in section 5.2. After all, a spatial crystal should break translational symmetry spontaneously while an edge breaks it explicitly. I would be grateful if the authors could clarify this point.
Final remark on content: At the very end of the text, the authors say "All integrations were performed numerically". I think that the authors should give a few more details, and in particular specify the integration algorithm.
I would like to see the above points clarified before I commit on a definite recommendation for SciPost Physics.
There are a few further minor issues that I list among the "Requested Changes".
Requested changes
1- Make the description of Fig. 1 more accessible.
2- Try to explain the content of section 2 better to a non-expert.
3- Define the angles $\vartheta$ and $\varphi$ properly and use this opportunity to specify the meaning of the "north pole".
4- Clarify if the "normal to" on line 2 of the caption of Fig. 5 is synonymous to "north".
5- The caption of Fig. 7 should mention that this space-time picture is for a chain of honeycomb cells.
6- Check if the terminology "nuclei" (several) versus "nucleus" (one) is used correctly in the video clip "adFig7.mp4".
7- Emphasize in the text that the "supplementary videos" are an integral part of this work.
8- Specify the source of in Ref. [49] (arXiv?) more clearly.
9- Clarify the notation ${\cal C} \otimes {\cal A}$, or possibly rather the meaning of ${\cal C} $ and ${\cal A}$, as appropriate.
10- Clarify the relevance of the edge in section 5.2 (Fig. 6(b)): in which sense is the resulting state still a crystal?
11- Expand the comment "All integrations were performed numerically" at the end of the Appendix. In particular, specify the integration algorithm.
12- Page 11: eliminate abbreviations that are not used again ("DO TC") or only a second time ("FDO").
13- Page 11: Using angles $\langle \cdot \rangle$ rather than less and bigger signs $<\cdot>$ for expectation values would improve readability.
14- Still page 11: The "timely" should probably rather be a "time" or "time-like".
15- Caption of Fig. 6: I think that "spatial" would be preferred spelling over "spacial".
16- Format Eq. (A3) such that the curly bracket "$\{$" stretches across both alternatives.
17- Last line of text: "effect" $\to$ "affect".
18- Properly upper-case names in the titles of Refs. [16,18,20,27,29,36,38,56].
19- Correct the spelling of the name of the author of Refs. [52,53]: "T. Prosen".
Report #1 by Anonymous (Referee 5) on 2022-7-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2203.04063v1, delivered 2022-06-30, doi: 10.21468/SciPost.Report.5313
Strengths
The paper introduces discrete time crystals based on the conformation of colloidal particles above a magnetic hexagonal pattern and subjected to external periodic field. The authors demonstrate complex periodic response of the system and dynamic phase transitions between reversible and non-reversible dynamic particle arrangements defined by the topology of the control loops driving the system. The complexity is further multiplied by the role of long-range multibody interactions and anisotropic filling of the cells.
Colloidal time crystal may introduce a powerful platform for topologically protected transport phenomena in driven colloidal ensembles.
Weaknesses
The paper is not easy to understand due to the complexity of the problem at hand. That is not a real weakness though. The authors tried their best to systematically introduce the required terminology and concepts.
Report
The paper addresses an important aspect of topology in space and time to generate a nontrivial dynamic response of the system on external periodic driving. The paper introduces concepts and approaches using the example of a magnetic colloidal system driven above the patterned magnetic substrates to demonstrate a rich variety of topological time crystalline and non-time crystalline phases phenomena available. I was humbled by the complexity of the system.
The paper is well written and suitable for publication in SciPost.
Requested changes
the paper introduces a lot of variables that are needed for the story, but some of them are not defined in time. For instance, on page 8 when defining \phi_A authors use vector a_1 that is not defined right away and only on page 10.
Krzysztof Sacha on 2022-05-01 [id 2423]
This work touches on an important problem of what we mean by classical time crystals. In the formation of quantum-time crystals, spontaneous breaking of the time translation symmetry is the key element. In classical mechanics the consequences of time translation symmetry are not that dramatic as in the quantum case. For example, time independent systems possess the continuous time translation symmetry, but any solution of classical equations of motion breaks this symmetry unless we consider a trivial situation of a particle at rest. Thus, breaking of the time translation symmetry in the classical case is not as surprising as spontaneous breaking of such a symmetry in the quantum many-body case. When we switch to periodically driven classical systems, especially many-body systems, then stable periodic evolution of the systems is highly nontrivial because it is related to ergodicity breaking. The present interesting work is related to such an important problem.